You most definitely have been sharing water with the cat for a long time now. My cat does that ALL of the time. We have just gotten used to it because we never know if she has weaseled her way to it or not. She likes to knock over the glass all of the time too. That irritates me sometimes, but the water drinking does not really bother me so much.
"You may have a dog that won't sit up, roll over or even cook breakfast, not because she's too stupid to learn how but because she's too smart to bother." - Rick Horowitz